As I said, control involves control over the mechanisms that control the mutation rate genome wide.
And yes, increasing mutation rates under stress is an advantageous response for a bacterial population because it increases the rate of evolution.
But the mutations are at specific locations in this genome wide endeavor. In any case, the mutations which do occur are part of a programmed response. If the locations are prone to exactly the same mutations, then those locations should by their very existence hit upon the same mutations produced during the induced hypermutation. So the ability to metabolize lactulose or lactose should be routinely "rediscovered" in the strain lacking the ability after a "few" more divisions.
But the mutations are at specific locations in this genome wide endeavor. In any case, the mutations which do occur are part of a programmed response. If the locations are prone to exactly the same mutations, then those locations should by their very existence hit upon the same mutations produced during the induced hypermutation. So the ability to metabolize lactulose or lactose should be routinely "rediscovered" in the strain lacking the ability after a "few" more divisions.